Abstract

A parallelisation of the fully-implicit fractional step based in-house DNS code was implemented. Utilising this, DNS of streamwise travelling waves of spanwise wall velocity in a turbulent channel flow were performed at Reτ = 200; 400; 800 and 1600, scaling the input parameters in wall units. Studying the drag reduction at varying Reynolds number showed that the maximum drag reduction decreased as Re was increased. The scaling with Reynolds number was dependent on the control parameters and therefore the optimal parameters changed with Re. An oscillation in the drag reduction over the forcing period was observed and associated with strong variations in the turbulent statistics, angling of the streaks and coherent structures, and the deterioration of the drag reduction. The conditionally averaged λ2 structures were found and behaved differently depending on the sign of the vorticity. This included a strong angling of the structure which rotated in agreement with the wall velocity, and this angle reduced over the half- period. The λ2 structures were moved away from the wall over the period, a feature also visible in the variation of the vorticity fluctuations. The relationship between the drag reduction and the extrema of the turbulent profiles were compared, and showed a good correlation between the maximum of the v rms profile and the DR achieved. This was seen to be independent of Reynolds number when the maximum v rms of the no control flow was subtracted. The variation of the power spent and net power saving with Reynolds number was also studied. The power spent scaled well with Reτ-0.16, and the net power saving scaled differently depending on the control parameters used. Although the maximum value was reduced as the Reynolds number increased.